The Multivariate Birnbaum-Saunders Distribution Based on a Asymmetric Distribution: EM-Estimation

Filidor Vilca
Camila Borelli Zeller
N. Balakrishnan

We derive here a multivariate generalization of the bivariate Birnbaum-Saunders (BS) distribution of Kundu et al. (2010) by basing it on the multivariate skew-normal (SN) distribution. The resulting multivariate Birnbaum-Saunders type distribution is an absolutely continuous distribution whose marginals are in the form of univariate Birnbaum-Saunders type distributions discussed by Vilca et al. (2011). We then study its characteristics and properties, such as the joint distribution function, marginal and conditional distributions. Next, we introduce a non-central multivariate BS distribution in order to present analytically a simple EM-algorithm for iteratively computing the maximum likelihood estimates of the model parameters, and compare the performance of this method with the estimation approach of Jamalizadeh and Kundu (2015). Moreover, the observed Fisher information matrix is analytically derived under the bivariate case, and some simulation studies and an application to a real data set are finally presented for the propose of illustrating the model and inferential results developed here.

Birnbaum-Saunders distribution; Skew-normal distribution; Marginal
RP 09/2018